In the figure,the value of the resistor to be connected between $C$ and $D$ so that the equivalent resistance of the entire circuit between $A$ and $B$ does not change with the number of elementary sets used is

Consider the two circuits $P$ and $Q$ shown below,which are used to measure the unknown resistance $R$. In each case,the resistance is estimated by using Ohm's law $R_{\text{est}} = \frac{V}{I}$,where $V$ and $I$ are the readings of the voltmeter and the ammeter,respectively. The meter resistances $R_V$ and $R_A$ are such that $R_A \ll R \ll R_V$. The internal resistance of the battery may be ignored. The absolute error in the estimate of the resistance is denoted by $\delta R = |R - R_{\text{est}}|$.
$(a)$ Express $\delta R_P$ in terms of the given resistance values.
$(b)$ Express $\delta R_Q$ in terms of the given resistance values.
$(c)$ For what value of $R$ will $\delta R_P \approx \delta R_Q$?

Under what conditions can the current passing through a resistance $R$ be increased by short-circuiting the battery of emf $E_2$? The internal resistances of the two batteries are $r_1$ and $r_2$ respectively.

The reading of the voltmeter in the circuit shown is ............. $V$. (in $.25$)

Two wires made of the same material have lengths in the ratio $2: 3$ and radii in the ratio $8: 9$. If the same potential difference is applied across the ends of the wires,the ratio of the electric currents flowing through them is

Consider the circuit given here with the following parameters: $E.M.F.$ of the cell = $12\, V$,internal resistance of the cell = $2\,\Omega$,and external resistance $R = 4\,\Omega$. Which one of the following statements is true?